The devices for the transfer of heat and/or mass of known construction consist of tubes or groups of tubes composed of a non-porous or porous material and embedded into a tube sheet. This tube sheet is fabricated either separately, in which case the tube ends must be fixed in the tube sheet at a later step, or the tube sheet is made during the manufacture of the heat and/or mass transferring apparatus by injecting a sealing compound between the tube ends. The manufacture of such heat and/or mass transferring devices is expensive, because either the tubes must be threaded into the tube sheet and positioned prior to fixing them therein, or special devices must be used to maintain the proper distance between the tube ends in order to be able to inject the sealing compound (self-curing material or plastic melt) between the tubes.